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Permutations

Tool to generate permutations of items, the arrangement of distinct items in all possible orders: 123,132,213,231,312,321.

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Permutations -

Tag(s) : Combinatorics

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Permutations

Permutations Generator






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Permutations with Repetition Generator

Partial Permutations Generator

⮞ Go to: K-Permutations

Combinations Generator

Permutations are often confused with combinations (n choose k). dCode has a tool for that:

Permutations/Anagrams Calculator




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Rank/Ordinal Number of a Permutation

Random Permutation

⮞ Go to: Random Selection

Answers to Questions (FAQ)

What is a permutation? (Definition)

In Mathematics, item permutations consist in the list of all possible arrangements (and ordering) of these elements in any order.

Example: The three letters A,B,C can be shuffled (anagrams) in 6 ways: A,B,C B,A,C C,A,B A,C,B B,C,A C,B,A

Permutations should not be confused with combinations (for which the order has no influence) or with arrangements also called partial permutations (k-permutations of some elements).

How to generate permutations?

The best-known method is the Heap algorithm (method used by this dCode's calculator).

Here is a pseudo code source : function permute(data, n) {
if (n = 1) print data
else {
for (i = 0 .. n-2) {
permute(data, n-1)
if (n % 2) swap(data[0], data[n-1])
else swap(data[i], data[n-1])
permute(data, n-1)
}
}
}

Permutations can thus be represented as a tree of permutations: permutation-tree

How to count permutations?

Counting permutations uses combinatorics and factorials

Example: For $ n $ items, the number of permutations is equal to $ n! $ (factorial of $ n $)

How to count distinguishable permutations?

Having a repeated item involves a division of the number of permutations by the number of permutations of these repeated items.

Example: DCODE 5 letters have $ 5! = 120 $ permutations but contain the letter D twice (these $ 2 $ letters D have $ 2! $ permutations), so divide the total number of permutations $ 5! $ by $ 2! $: $ 5!/2!=60 $ distinct permutations.

Source code

dCode retains ownership of the "Permutations" source code. Except explicit open source licence (indicated Creative Commons / free), the "Permutations" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Permutations" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Permutations" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
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Cite as source (bibliography):
Permutations on dCode.fr [online website], retrieved on 2024-07-15, https://www.dcode.fr/permutations-generator

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